Acknowledgements Thanks for feedback on various versions and parts of this presentation (the long version has all parts, hence gapless slide numbers):

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Presentation on theme: "Acknowledgements Thanks for feedback on various versions and parts of this presentation (the long version has all parts, hence gapless slide numbers):"— Presentation transcript:

2 AbstractDirected labeled graphs (DLGs) provide a good starting point for visual data & knowledge representation but cannot straightforwardly represent nested structures, non-binary relationships, and relation descriptions. These advanced features require encoded constructs with auxiliary nodes and relationships, which also need to be kept separate from straightforward constructs. Therefore, various extensions of DLGs have been proposed for data & knowledge representation, including graph partitionings (possibly interfaced as complex nodes), n-ary relationships as directed labeled hyperarcs, and (hyper)arc labels used as nodes of other (hyper)arcs. Meanwhile, a lot of AI / Semantic Web research and development on ontologies & rules has gone into extended logics for knowledge representation such as object (frame) logics, description logics, general modal logics, and higher-order logics. The slides demonstrate how data & knowledge representation with graphs and logics can be reconciled. They proceed from simple to extended graphs for logics needed in AI and the Semantic Web. Along with its visual introduction, each graph construct is mapped to its corresponding symbolic logic construct. These graph-logic extensions constitute a systematics defined by orthogonal axes, which has led to the Grailog 1.0 language as part of the Web-rule industry standard RuleML 1.0 ( While Grailog's DLG sublanguage corresponds to binary-associative memories, its hypergraph sublanguage corresponds to n-ary content-addressable memories, and its complex-node modules offer various further opportunities for parallel processing

9 Note on Grailog and API4KBBesides mapping Grailog to/fro RuleML, RDF and UML+OCL can be targeted, with uniform access to be provided by API4KBGrailog and API4KB strive to cover main data & knowledge representation paradigms:RDF (directed-labeled-graph) and Relational (Datalog-fact-like) dataOntology (RDFS and description-logic) and Rule (Horn- and general-logic) knowledgeAn API can be (initially) designed and tested with a human in the loop much like a GUI

10 Generalized Graphs to Represent and Map Logic Languages According to Grailog 1.0 SystematicsWe have used generalized graphs for representing various logic languages, where basically:Graph nodes (vertices) represent individuals, classes, etc.Graph arcs (edges) represent relationshipsNext slides: What are the principles of this representation and what graph generalizations are required?Later slides: How are these graphs mapped (invertibly) to logic, thus specifying Grailog as a ‘GUI’ for knowledge?Final slides: What is the systematics of Grailog features?

11 Grailog PrinciplesGraphs should make it easier for humans to read and write logic constructs via 2D state-of-the-art representation with shorthand & normal forms, from Controlled English to logicGraphs should be natural extensions (e.g. n-ary) of Directed Labeled Graphs (DLGs), often used to represent simple semantic nets, i.e. of atomic ground formulas in function-free dyadic predicate logic (cf. binary Datalog ground facts, RDF triples, the Open Graph, and the Knowledge Graph)Graphs should allow stepwise refinements for all logic constructs: Description Logic constructors, F-logic frames, general PSOA RuleML terms, etc.Extensions to boxes & links should be orthogonal

12 Informal Grailog Preview: Searle’s Chinese Room ArgumentJohn Searle (emphasis added):“... whatever purely formal principles you put into the computer, they will not be sufficient for understanding, since a human will be able to follow the formal principles without understanding anything.” (Minds, Brains and Programs, 1980)

42 From Hyperarc Crossings to Node Copies as a Normalization Sequence (1Hypergraph (2 hyperarcs,parallel-cuttinga node)DLG (4 arcs, do not specifyto whom Latinis shown or taught)ShowtoJohnShowLatinKateJohnLatinKateMaryPaulMaryPaulTeachTeachtoThe hyperarc for, e.g., ternary Show(John,Latin,Kate) can be seen as the path composition of 2 arcs for binary Show(John,Latin) and binary to(Latin,Kate)

61 Graphical Elements: Arrows (2)Arrows for special arcs and hyperarcsHasInstance: Connects class, as labelnode, with instance (hyperarc of length 1)As in DRLHs and shown earlier, labelnodes can also be used (instead of labels) for hyperarcs of length > 1SubClassOf: Connects subclass, unlabeled, with superclass (arc, i.e. of length 2)Implies: Hyperarc from premise(s) to conclusionObject-IDentified slots and shelves: Bulleted arcs and hyperarcs

105 Beliefs and Desires as Propositional Attitudes (1)Propositional attitude: a mental state relating a person to a proposition (which can involve other persons)“If George desires action A and believes (the proposition) that originator O will cause A, then George supports O.”AdesireObelievecauseGrailog:Georgesupport

106 Beliefs and Desires as Propositional Attitudes (2)Example: “If John desires the negation of (state of affairs) X, then he does not desire X.”desiredesireXJohnGrailog:While variables A and O of the earlier example are bound toan action and originator individual, variable X here is bound toan entire proposition or an arbitrarily complex set of propositions